Radium in groundwater can become a serious health concern if the concentrations become high enough. Radium is a decay product of uranium and is therefore found wherever uranium might be found. It is over one million times more radioactive than uranium. Radium decays radioactively predominately giving off alpha particles but different decay pathways also generate beta particles and gamma rays.
One significant danger of radium in drinking water is that it is chemically similar to calcium and can replace calcium in bones. Exposure to radium, either internally or, to a lesser degree, externally, can cause cancer and other radiation exposure disorders. Working with radium, and its decay product, radon gas, has been blamed for Marie Curie's death due to destruction of the ability of her bone marrow to create new blood cells.
Since radium can be stored in the body in replacement to calcium, and radiation damage is in many ways cumulative over a lifetime, significant quantities of radium in drinking water are a serious concern. Studies have shown clear correlations between concentrations of radium in drinking water and leukemia and other cancers.
Since the primary decay of radium is through alpha particles, the greatest danger is through ingestion or inhalation of radium. Alpha particles are relatively low energy particles consisting of two neutrons and two protons, essentially helium nuclei. Given their comparatively significant mass, low energy and strong electromagnetic properties, alpha particles can be stopped by as little as a sheet of paper. Because of this, clothing and the skin provide significant protection from external exposure.
In drinking water, however, radium is consumed and a small portion can stay in the body indefinitely. Most ingested radium is passed through the body unchanged while some will be excreted through urine. A small portion of all ingested radium, however, will be stored in the body and, if that amount is significant enough over time, it can cause significant health risks.
Radium is mostly found in very deep aquifers, those close to the sources of the radium itself. Deep aquifers located on top of igneous rock can have significant enough concentrations of radium to be of concern. Shallower aquifers and those that don't pass near a source of radium can usually be considered safe.
Radium can be removed from drinking water through as number of methods. Ion exchange methods, also known as water softeners, can replace radium, along with calcium and magnesium, in water. However, this is accomplished by replacing those ions with sodium, which can have its own concerns. Distillation and reverse osmosis will also remove radium and other contaminants from water but at the cost of greater energy usage.
If you get your water from a municipal or other public water supply you might check with your supplier to see what their water testing has shown in regards to radium contamination. The EPA has guidelines for what is allowable so this testing should be done on a regular basis and you can be reasonably assured that your water is safe. If you use water from your own well, if that well is fairly shallow and not near igneous rock that might serve as a source of radium again you can be relatively confident that your water is safe to drink in regards to radium. If, however, you live in a region with large masses of granite or other igneous rocks, or if you have a very deep well from which you get your drinking water, it would recommended that you have that water tested on a regular basis.